Exercise 11.4
Given a cylindrical tank, in which situation will you find surface area and in which situation volume.
(a) To find how much it can hold
(b) Number of cement bags required to plaster it
(c) To find the number of smaller tanks that can be filled with water from it.
Sol :
(a) In this situation, we will find the volume.
(b) In this situation, we will find the surface area.
(c) In this situation, we will find the volume.
Q 2 - Ex 11.4 - Mensuration - NCERT Maths Class 8th - Chapter 11
Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?
Sol :
The heights and diameters of these cylinders A and B are interchanged.
We know that,
Volume of cylinder
If measures of r and h are same, then the cylinder with greater radius will have greater area.
Radius of cylinder A =
cmRadius of cylinder B =
cm = 7 cmAs the radius of cylinder B is greater, therefore, the volume of cylinder B will be greater.
Let us verify it by calculating the volume of both the cylinders.
Volume of cylinder A
Volume of cylinder B
Volume of cylinder B is greater.
Surface area of cylinder A
Surface area of cylinder B
Thus, the surface area of cylinder B is also greater than the surface area of cylinder A.
Q 3 - Ex 11.4 - Mensuration - NCERT Maths Class 8th - Chapter 11
Question 3
Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3?
Sol :
Base area of the cuboid = Length × Breadth = 180 cm2
Volume of cuboid = Length × Breadth × Height
900 cm3 = 180 cm2 × Height
Thus, the height of the cuboid is 5 cm.
Question 4
A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
Sol :
Volume of cuboid = 60 cm × 54 cm × 30 cm = 97200 cm3
Side of the cube = 6 cm
Volume of the cube = (6)3 cm3 = 216 cm3
Required number of cubes =
Thus, 450 cubes can be placed in the given cuboid.
Q 5 - Ex 11.4 - Mensuration - NCERT Maths Class 8th - Chapter 11
Question 5
Find the height of the cylinder whose volume is 1.54 m3 and diameter of the base is 140 cm?
Sol :
Diameter of the base = 140 cm
Radius (r) of the base
Volume of cylinder
Thus, the height of the cylinder is 1 m.
Q 6 - Ex 11.4 - Mensuration - NCERT Maths Class 8th - Chapter 11
A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres that can be stored in the tank?
Sol :
Length of cylinder = 7 m
Volume of cylinder
1m3 = 1000 L
Required quantity = (49.5 × 1000) L = 49500 L
Therefore, 49500 L of milk can be stored in the tank.
Q 7 - Ex 11.4 - Mensuration - NCERT Maths Class 8th - Chapter 11
Question 7
If each edge of a cube is doubled,
(i) how many times will its surface area increase?
(ii) how many times will its volume increase?
Sol :
(i) Let initially the edge of the cube be l.
Initial surface area = 6l2
If each edge of the cube is doubled, then it becomes 2l.
New surface area = 6(2l)2 = 24l2 = 4 × 6l2
Clearly, the surface area will be increased by 4 times.
(ii) Initial volume of the cube = l3
When each edge of the cube is doubled, it becomes 2l.
New volume = (2l)3 = 8l3 = 8 × l3
Clearly, the volume of the cube will be increased by 8 times.
Q 8 - Ex 11.4 - Mensuration - NCERT Maths Class 8th - Chapter 11
Question 8
Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m3, find the number of hours it will take to fill the reservoir.
Sol :
Volume of cuboidal reservoir = 108 m3 = (108 × 1000) L = 108000 L
It is given that water is being poured at the rate of 60 L per minute.
That is, (60 × 60) L = 3600 L per hour
Required number of hours
= 30 hoursThus, it will take 30 hours to fill the reservoir.
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